A gyrator is a passive, linear, lossless, two-port electrical network element proposed in 1948 by Bernard D. H. Tellegen as a hypothetical fifth linear element after the passive network elements of the resistor, capacitor, inductor, and ideal transformer. Unlike these elements, the gyrator is non-reciprocal. By virtue of Tellegen's theorem, any multiport network formed by combinations of resistor, capacitor, inductor, and ideal transformer elements has a symmetrical S-parameters matrix, and therefore meets the principle of reciprocity. Reciprocity is the relationship between an oscillating (e.g., alternating) current and the resulting electric field, which remains unchanged if one interchanges the points where the current is placed and where the field is measured. For the specific case of an electrical network, it may also be said that voltages and currents at different points in the network can be interchanged.
A non-reciprocal device like a gyrator, on the other hand, is a device that transmits a signal unchanged in the forward direction between two ports, but reverses the polarity of the signal traveling in the backward direction, e.g., resulting in a 180° phase-shift in the backward traveling signal as compared to the forward direction.
As it was envisioned in the 1940s, the properties of magnetic materials can be exploited to build passive devices that break the principle of reciprocity. Such passive devices may include, for example, gyrators and circulators. A circulator is a passive non-reciprocal three-port or four-port device, in which a microwave or radio frequency signal entering any port is transmitted only to the next port in rotation. A port in this context is a point where an external waveguide or transmission line (such as a microstrip line or a coaxial cable), connects to the device. For a three-port circulator, a signal applied to port 1 only comes out of port 2; a signal applied to port 2 only comes out of port 3; a signal applied to port 3 only comes out of port 1, so to within a phase-factor, the scattering matrix for an ideal three-port circulator is:
  S  =            (                                    0                                0                                1                                                1                                0                                0                                                0                                1                                0                              )        .  
Circulators based on ferrites are currently widespread. The main limitation of these devices is their electromagnetic (EM) wavelengths, particularly at lower RF frequencies, e.g., less than 1.5 GHz. Circulators based on ferrites, however, are too large and are certainly incompatible with use at chip scale, e.g., within integrated circuits.
Recent attempts of getting size-manageable non-reciprocal devices are based on modulation. These approaches suffer from noise introduced by dynamic biasing sources (phase noise in oscillators or jitter in the clocks) or noise folding effect due to harmonics. Furthermore, these approaches produce either the intermodulation between in-band signals due to the nonlinear capacitance/voltage curve of the varactors, or cross-modulations between in-band signals and the basing (and their harmonics) due to the switching-enabled modulation. These effects present new challenges that are germane to active device techniques.